How can I break apart a mountain in Blender?
You could try out the Fracture Modifier Build

from here... http://df-vfx.de/fracturemodifier/

or here http://graphicall.org/1148

which is a separate blender build.

I closed the bottom of the landscape with a face, then I prefractured this with a helper object and Voronoi + Boolean. After that i set up some easily breakable constraints and triggering, and added a ground plane.

Simulation looks like this:



If you have further questions, please post either here on stackexchange or here :

https://blenderartists.org/forum/showthread.php?343637-Custom-Build-Blender-Fracture-Modifier

The Blend link: (will only work with the Fracture Modifier Build)